Finite Group Databasebeta

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C11×C17×D31⋊C3 #46852035

order34782
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC11×C17×D31⋊C3
unambiguous semidirect productD31⋊(C3×C11×C17)
unambiguous semidirect product(C31⋊C3)⋊(C2×C11×C17)
unambiguous semidirect product(C11×D31)⋊(C3×C17)
unambiguous semidirect product(C17×D31)⋊(C3×C11)
unambiguous semidirect product(C11×C17×D31)⋊C3

Splittings

Fitting, socle, HallC11×C17×C31 ⋊ C2×C3
derived, SylowC31 ⋊ C2×C3×C11×C17
HallC11×C17×C31⋊C3 ⋊ C2
HallC11×C17×D31 ⋊ C3
HallC17×C31⋊C3 ⋊ C2×C11
HallC17×D31 ⋊ C3×C11
HallC11×C31⋊C3 ⋊ C2×C17
HallC11×D31 ⋊ C3×C17
HallC17×C31 ⋊ C2×C3×C11
HallC11×C31 ⋊ C2×C3×C17
HallC31⋊C3 ⋊ C2×C11×C17
HallD31 ⋊ C3×C11×C17

Subgroups

subgroupG/H
center, hypercenterC11×C17D31⋊C3
commutator, cosocle, hypocenterC31C2×C3×C11×C17
FrattiniC1G
Fitting, socleC11×C17×C31C2×C3
LCSG ▷ C31
UCSC1 ◁ C11×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5797

Conjugacy classes & character table

2057 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34782, 18);